Deep Learning Over Reduced Intrinsic Domains for Efficient Mechanics of the Left Ventricle

Talou, Gonzalo D. Maso; Gamage, Thiranja P. Babarenda; Sagar, Mark; Nash, Martyn P.

doi:10.3389/fphy.2020.00030

Cited by 13 publications

(16 citation statements)

References 27 publications

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“…From the FE mechanical model defined in section 2.1, we derive a surrogate model as described in Maso Talou et al ( 2020 ). The AI-surrogate model predicts the displacement of a material point x = ( x d , y d , z d ) for a given intra-ventricular pressure p , domain description g = ( g 1 , g 2 ) (PCA weights as explained in Maso Talou et al, 2020 ) and the constitutive parameters ( c 1 , c 2 ). Particularly, we fixed parameters c 3 = 3.67 and c 4 = 25.77 as their identifiability from macro-scale observations is low.…”

Section: Methodsmentioning

confidence: 99%

“…where

and

define sets of points (training batches) on the basal/endocardial boundary (where Dirichlet or Neumann boundary conditions were applied) and inside the domain, respectively, u i and

are the displacements predicted with the neural network and the FE model, respectively, α = 4.5 is the penalty factor to impose the boundary conditions, and

is a given training batch. For further details about the training of the AI-surrogate, refer to (Maso Talou et al, 2020 ).…”

Section: Methodsmentioning

confidence: 99%

“…In this work, we propose two strategies to identify inputs of the surrogate model from a given set of observations of ventricular kinematics from medical images. As presented in our previous work (Maso Talou et al, 2020 ), we can encode boundary conditions, applied tractions, domain geometry and constitutive parameters as inputs of these networks, thus the proposed techniques can be used to characterise any of these inputs.…”

Section: Methodsmentioning

confidence: 99%

“…Surrogate models have been developed to improve simulation efficiency, replacing computationally expensive FE simulations with inexpensive surrogate simulations (Dabiri et al, 2019 ; Maso Talou et al, 2020 ; Cai et al, 2021 ). These surrogate models have also been used to accelerate calibration procedures (Di Achille et al, 2018 ; Davies et al, 2019 ; Noe et al, 2019 ; Longobardi et al, 2020 ; Cai et al, 2021 ).…”

Section: Introductionmentioning

confidence: 99%

“…In this work, we propose a novel approach that uses AI-surrogate model and automatic differentiation to efficiently identify constitutive parameters or loading conditions of a biomechanical model given kinematic measurements from medical images. This builds upon our recent work in developing deep learning approaches that substantially reduce the computational cost of simulating cardiac biomechanics, by training an AI-surrogate model that accurately reproduces mechanics predictions with a fraction of the computational cost of numerical methods that solve the governing partial differential equations (Maso Talou et al, 2020 ). We demonstrate this approach for estimating passive stiffness or pressure of the left ventricle (LV).…”

Section: Introductionmentioning

confidence: 99%

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Efficient Ventricular Parameter Estimation Using AI-Surrogate Models

2021

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The onset and progression of pathological heart conditions, such as cardiomyopathy or heart failure, affect its mechanical behaviour due to the remodelling of the myocardial tissues to preserve its functional response. Identification of the constitutive properties of heart tissues could provide useful biomarkers to diagnose and assess the progression of disease. We have previously demonstrated the utility of efficient AI-surrogate models to simulate passive cardiac mechanics. Here, we propose the use of this surrogate model for the identification of myocardial mechanical properties and intra-ventricular pressure by solving an inverse problem with two novel AI-based approaches. Our analysis concluded that: (i) both approaches were robust toward Gaussian noise when the ventricle data for multiple loading conditions were combined; and (ii) estimates of one and two parameters could be obtained in less than 9 and 18 s, respectively. The proposed technique yields a viable option for the translation of cardiac mechanics simulations and biophysical parameter identification methods into the clinic to improve the diagnosis and treatment of heart pathologies. In addition, the proposed estimation techniques are general and can be straightforwardly translated to other applications involving different anatomical structures.

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Section: Methodsmentioning

confidence: 99%

“…where

and

define sets of points (training batches) on the basal/endocardial boundary (where Dirichlet or Neumann boundary conditions were applied) and inside the domain, respectively, u i and

are the displacements predicted with the neural network and the FE model, respectively, α = 4.5 is the penalty factor to impose the boundary conditions, and

is a given training batch. For further details about the training of the AI-surrogate, refer to (Maso Talou et al, 2020 ).…”

Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Efficient Ventricular Parameter Estimation Using AI-Surrogate Models

2021

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Bayesian optimisation for efficient parameter inference in a cardiac mechanics model of the left ventricle

Borowska

Gao

Lazarus

et al. 2022

Numer Methods Biomed Eng

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We consider parameter inference in cardio‐mechanic models of the left ventricle, in particular the one based on the Holtzapfel‐Ogden (HO) constitutive law, using clinical in vivo data. The equations underlying these models do not admit closed form solutions and hence need to be solved numerically. These numerical procedures are computationally expensive making computational run times associated with numerical optimisation or sampling excessive for the uptake of the models in the clinical practice. To address this issue, we adopt the framework of Bayesian optimisation (BO), which is an efficient statistical technique of global optimisation. BO seeks the optimum of an unknown black‐box function by sequentially training a statistical surrogate‐model and using it to select the next query point by leveraging the associated exploration‐exploitation trade‐off. To guarantee that the estimates based on the in vivo data are realistic also for high‐pressures, unobservable in vivo, we include a penalty term based on a previously published empirical law developed using ex vivo data. Two case studies based on real data demonstrate that the proposed BO procedure outperforms the state‐of‐the‐art inference algorithm for the HO constitutive law.

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Efficient approximation of cardiac mechanics through reduced‐order modeling with deep learning‐based operator approximation

Cicci,

Fresca,

Manzoni

et al. 2023

Numer Methods Biomed Eng

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Reducing the computational time required by high‐fidelity, full‐order models (FOMs) for the solution of problems in cardiac mechanics is crucial to allow the translation of patient‐specific simulations into clinical practice. Indeed, while FOMs, such as those based on the finite element method, provide valuable information on the cardiac mechanical function, accurate numerical results can be obtained at the price of very fine spatio‐temporal discretizations. As a matter of fact, simulating even just a few heartbeats can require up to hours of wall time on high‐performance computing architectures. In addition, cardiac models usually depend on a set of input parameters that are calibrated in order to explore multiple virtual scenarios. To compute reliable solutions at a greatly reduced computational cost, we rely on a reduced basis method empowered with a new deep learning‐based operator approximation, which we refer to as Deep‐HyROMnet technique. Our strategy combines a projection‐based POD‐Galerkin method with deep neural networks for the approximation of (reduced) nonlinear operators, overcoming the typical computational bottleneck associated with standard hyper‐reduction techniques employed in reduced‐order models (ROMs) for nonlinear parametrized systems. This method can provide extremely accurate approximations to parametrized cardiac mechanics problems, such as in the case of the complete cardiac cycle in a patient‐specific left ventricle geometry. In this respect, a 3D model for tissue mechanics is coupled with a 0D model for external blood circulation; active force generation is provided through an adjustable parameter‐dependent surrogate model as input to the tissue 3D model. The proposed strategy is shown to outperform classical projection‐based ROMs, in terms of orders of magnitude of computational speed‐up, and to return accurate pressure‐volume loops in both physiological and pathological cases. Finally, an application to a forward uncertainty quantification analysis, unaffordable if relying on a FOM, is considered, involving output quantities of interest such as, for example, the ejection fraction or the maximal rate of change in pressure in the left ventricle.

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Deep Learning Over Reduced Intrinsic Domains for Efficient Mechanics of the Left Ventricle

Cited by 13 publications

References 27 publications

Efficient Ventricular Parameter Estimation Using AI-Surrogate Models

Efficient Ventricular Parameter Estimation Using AI-Surrogate Models

Bayesian optimisation for efficient parameter inference in a cardiac mechanics model of the left ventricle

Efficient approximation of cardiac mechanics through reduced‐order modeling with deep learning‐based operator approximation

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